Programmers! Have you been asked to solve a computationally intractable task?

And do you ever solve algorithmic problems?

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Readers' corner And so to El Reg forums, where Julian Bradfield, an academic, writes:

In a vigorous discussion about revising courses in a computer science degree, one of my colleagues opined that "every decent programmer is sometime going to come across a task that is NP-hard, so they need to know to tackle NP-hard problems".

I'm curious as to whether anybody on here (who is a programmer after going through a so-called top university's computer science degree) has ever been asked to solve a task that is computationally intractable, and if so whether they used the last couple of decades' work on such things to solve it. Come to that, how many CS graduates ever solve algorithmic problems, rather than systems engineering problems?